Block #1,591,965

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/19/2016, 9:05:25 PM · Difficulty 10.6531 · 5,235,294 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

da9272eb66ad4aaf7e1ed0d79fe58bb49cbd5076a82e0ee4b49370f0b23f7390

View on Chainz ↗

Height

#1,591,965

Difficulty

10.653076

Transactions

Size

1.54 KB

Version

Bits

0aa72fff

Nonce

673,732,991

Timestamp

5/19/2016, 9:05:25 PM

Confirmations

5,235,294

Mined by

⛏️ P2SHARdy5X3X6K1nmHN19eZaN8wbR56nDXEzNY

Merkle Root

8c092e27c3e0f193027ed4d70ef6b0b1e53ec03705a0acfd38ad35434469eb92

Transactions (2)

Coinbasea507ec04ee7bfc…770ac39322bfad

1 in → 1 out8.8200 XPM110 B

ARdy5X3X…6nDXEzNY

c6a26a4b8d91aa…9eb94cd4516589

1 in → 36 out131.5913 XPM1.35 KB

AZqU9K1n…q9nSDZkU ANvuCGwS…xfZ7fmUM AbwijVU5…qRbvEC24 ARtizRYz…4FSN5vJA AN2t8qHh…oRP5WsRw

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.547 × 10⁹⁷(98-digit number)

35473303358139296695…74037296549136302079

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

3.547 × 10⁹⁷(98-digit number)

35473303358139296695…74037296549136302079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.547 × 10⁹⁷(98-digit number)

35473303358139296695…74037296549136302081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

7.094 × 10⁹⁷(98-digit number)

70946606716278593391…48074593098272604159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.094 × 10⁹⁷(98-digit number)

70946606716278593391…48074593098272604161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.418 × 10⁹⁸(99-digit number)

14189321343255718678…96149186196545208319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.418 × 10⁹⁸(99-digit number)

14189321343255718678…96149186196545208321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.837 × 10⁹⁸(99-digit number)

28378642686511437356…92298372393090416639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.837 × 10⁹⁸(99-digit number)

28378642686511437356…92298372393090416641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

5.675 × 10⁹⁸(99-digit number)

56757285373022874713…84596744786180833279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.675 × 10⁹⁸(99-digit number)

56757285373022874713…84596744786180833281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,591,965

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